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arXiv:2302.14232 · Physical Review Research

Quantum phases in spin-orbit-coupled Floquet spinor Bose gases

Yani Zhang, Yuanyuan Chen, Hao Lyu, Yongping Zhang

Published Jun 13, 2023• 13 citations
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Abstract

We propose a spin-orbit-coupled Floquet spinor Bose-Einstein condensate (BEC) which can be implemented by Floquet engineering of a quadratic Zeeman field. The Floquet spinor BEC has a Bessel-function-modulated Rabi frequency and a Floquet-induced spin-exchange interaction. The quantum phase diagram of the spin-orbit-coupled Floquet spinor BEC is investigated by considering antiferromagnetic or ferromagnetic spin-spin interactions. In comparison with the usual spin-orbit-coupled spin-1 BEC, we find that a stripe phase for antiferromagnetic interactions can exist in a large quadratic Zeeman field regime, and a different stripe phase with an experimentally favorable contrast for ferromagnetic interactions is uncovered.

DOI
10.1103/physrevresearch.5.023160

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We study elementary excitations in a Floquet-engineered spin-1 BEC with spin–orbit coupling, which can be realized by periodically driving the quadratic Zeeman shift. We calculate the excitation spectrum of the plane-wave phase, the zero-momentum phase, and the stripe phase, as well as the corresponding response function and static structure factor. In special, we find that two roton modes appear in the lowest two excitation bands of the stripe phase, which are tunable by changing the driving parameters. The phase transition between different phases can be identified by the sound velocity of these phases. We also investigate spin dynamics in such a system, which strongly depend on the driving parameter.
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Abstract While a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) has been experimentally observed, its elementary excitations remain unclear in the stripe phase. Here, we systematically study the elementary excitations in three distinct phases of a spin–orbit-coupled spin-1 BEC. We find that the excitation spectrum as well as the corresponding static response function and structure factor depend strongly on spin–orbit coupling parameters such as the quadratic Zeeman field and the Rabi frequency. In the stripe phase, besides two gapless Goldstone modes, we show the existence of roton excitations. Finally, we demonstrate that quantum phase transitions between these different phases including the zero-momentum, plane wave and stripe phases are characterized by the sound velocities and the quantum depletion.
The recent experimental realization of spin-orbit (SO) coupling for spin-1 ultracold atoms opens an interesting avenue for exploring SO-coupling-related physics in large-spin systems, which is generally unattainable in electronic materials. In this paper, we study the effects of interactions between atoms on the ground states and collective excitations of SO-coupled spin-1 Bose-Einstein condensates (BECs) in the presence of a spin-tensor potential. We find that ferromagnetic interaction between atoms can induce a stripe phase exhibiting in-phase or out-of-phase modulating patterns between spin-tensor and zero-spin-component density waves. We characterize the phase transitions between different phases using the spin-tensor density as well as the collective dipole motion of the BEC. We show that there exists a double maxon-roton structure in the Bogoliubov-excitation spectrum, attributed to the three band minima of the SO-coupled spin-1 BEC.
We numerically investigate the ground state phases and quench dynamics of spin-orbit coupled spin-1 Bose-Einstein condensates with ferromagnetic and antiferromagnetic interactions. For finite Rabi coupling, the system exhibits zero-momentum, elongated zero-momentum, and stripe phases, while in the limit Ω→0Ω\rightarrow 0Ω→0, the superstripe wave phases emerge. Varying the attractive density-density (c0c_0c0​) and spin-exchange (c2c_2c2​) interactions induces the transition from stripe and superstripe phases to the elongated zero-momentum phase, characterized by miscibility and polarization. The condensate remains miscible in the zero-momentum phase and partially miscible for the elongated, stripe, and superstripe phases. Quenching in Rabi coupling stabilizes the condensate, while spin-orbit coupling quenching leads to fluctuations or the formation of complex patterns, with the stripe phase exhibiting the vanishing of the zeroth spin component over time. Our results may offer valuable insights into engineering exotic quantum phases in ultracold atomic gases.